Segmented variable-frequency ultrasound synergistic hot-air drying of Rhubarb: Effect on drying characteristics and quality and thermal analysis

Graphical abstract


Introduction
Rhubarb, belonging to the genus Rheum in the family Polygonaceae, is a collective term encompassing the roots and rhizomes of Rheum palmatum L., R.tanguticum Maxim.exBalf.or R.officinale Baill.(medicinalRhubarb) [1].It is rich in nutrients and contains polyphenols, flavonoids, phytosterols, anthraquinone derivatives, anthraquinone glycosides, tannins, and other substances.Modern pharmacological studies have revealed that Rhubarb possesses a significant medicinal value due to its effects, such as inducing laxation, protecting the liver and kidneys, as well as exerting anti-inflammatory and anti-allergic properties [2][3][4][5].However, due to its high moisture content, improper storage of Rhubarb can lead to issues such as rotting, browning, and, importantly, the loss of natural active ingredients such as anthraquinones.The drying process effectively inhibits the proliferation of microorganisms and enzyme activity in Rhubarb, thereby reducing the occurrence of physical and chemical reactions during storage.This preservation method significantly enhances the retention of natural active ingredients.Therefore, drying plays a pivotal role in the industrial production of Rhubarb.
Currently, the standard drying methods for Rhubarb are traditional sun-drying (SD) and smoke drying (SMD).However, SD entails prolonged drying cycles and is susceptible to weather fluctuations, while SMD poses environmental pollution risks and demands substantial labor input [6].Consequently, there exists a pressing need to investigate a highly efficient and resource-conserving drying method and process for Rhubarb.Hot-air drying (HAD) is a viable alternative method, but its development is hindered by issues such as low heat transfer efficiency and extended deceleration period [7].In agricultural product drying production, the advent of innovative hot air combined drying technology has significantly enhanced overall efficiency and upheld product quality, rendering it a pivotal frontier in drying technology evolution.
Ultrasound technology, renowned for its profound penetration and robust energy transmission capabilities, propagates longitudinal waves in gases, liquids, and solids, as well as transverse waves with shear force within solid mediums [8].Ultrasound propagation engenders a spectrum of effects spanning thermal, mechanical, chemical, and cavitation phenomena.Cavitation, in particular, catalyzes a range of consequential mechanisms, including radiation force, shock wave propagation, microjet formation, and material deformation [8].Currently, ultrasound technology is used extensively in food processing, such as cleaning materials, sterilization, and aiding in drying processes.Among these applications, ultrasound-assisted drying stands out as a crucial dewatering method.It accelerates external heat transfer while reducing internal mass transfer resistance [9].Relevant studies have indicated that ultrasound-assisted drying not only accelerates the drying process but also amplifies the energy production efficiency and biodegradability of wastewater in fruit drying processes [10,11].Ultrasound synergistic hotair drying represents a sophisticated amalgamation wherein ultrasonic waves impart acoustic pressure onto materials, instigating thermal effects and synergistically interacting with hot air currents to induce desiccation [9].Unlike conventional hot-air drying, this method operates at lower temperatures, rendering it especially conducive to materials harboring thermosensitive natural constituents, thus yielding superior product integrity [9].Ultrasound synergistic hot-air drying not only accelerates the drying rate and conserves energy but also enhances the quality of dried products.This demonstrates significant potential for widespread application [12].In the research realm of ultrasound synergistic hot-air drying, studies by Liu et al. [13] have demonstrated that this method can expedite mass transfer within materials while reducing energy consumption.Moreover, Thanompongchart et al. [14] have confirmed that ultrasound synergistic hot-air drying can bolster the moisture evaporation rate of pineapple slices.
In recent years, ultrasound applications in food processing have primarily focused on single-frequency or multiple-frequency constantfrequency ultrasounds.However, a holistic assessment reveals that single-frequency ultrasound drying manifests a sluggish drying rate, feeble ultrasonic cavitation effect, and uneven energy dissipation [15].In comparison, multi-frequency ultrasound improves the uniformity of the sound field and enhances the cavitation effect over single-frequency ultrasound.Nevertheless, multi-frequency ultrasound consumes more energy, has poor economic efficiency, and causes significant damage to the internal structure of materials [16].Furthermore, the prolonged emission of constant-frequency ultrasonic waves not only fails to maximize the ultrasonic resonance-induced effects but also needs to improve in enhancing material drying characteristics and quality [17].Therefore, it is necessary to explore an ultrasound-assisted modality with a more integrated effect.Variable-frequency ultrasound is a mode of ultrasound action in which the frequency is regularly shifted at specific time points.Currently, variable-frequency ultrasound has demonstrated promising applications in optimizing the extraction process of rose polyphenols and facilitating the enzymatic hydrolysis reaction of rapeseed protein [18,19].In addition, the utilization of alternating dualfrequency variable-frequency ultrasound in drying pretreatment underscores its high feasibility in the food processing stage [20].However, there are fewer studies on the synergistic effect of variable-frequency ultrasound with other drying techniques, leaving unexplored whether altering ultrasound frequencies can yield improved drying characteristics and superior quality of dried products.For this reason, this study set the ultrasonic frequency in segments on the basis of the single-frequency test and investigated the effects of segmented variable-frequency ultrasound synergistic hot-air drying (SVFU-HAD) on the drying characteristics of Rhubarb, color difference, natural active ingredients, rehydration ratio, microstructure, and the temperature change of the heat transfer process, aiming to delineate a more efficacious ultrasound synergistic hot-air drying process for Rhubarb slices.

Experimental materials
The experiment selected Rhubarb (Rheum palmatum L.) grown in Hui County planting base in Longnan City, Gansu Province.Fresh Rhubarb of similar size without diseases or pests was chosen.The average initial moisture content of fresh Rhubarb was 69.47% ± 0.50% (HKSF-2 rapid moisture analyzer, Wuxi Huake Instrument Co., Ltd., Wuxi, China), and then the Rhubarb was stored in a constant temperature and humidity chamber (4 • C) after purchase.

Experimental method
The Rhubarb was sliced (horizontally) and measured using a vernier caliper to ensure a thickness range of (4 ± 0.5) mm.Subsequently, the slices were methodically arranged in a random and uniform manner on a drying tray, with each group meticulously weighed to fall within the specified range of (120 ± 1) g (electronic analytical balance, Yuyao Jiming Weighing Verification Equipment Co., Ltd., Yuyao, China).Following a rigorous 20-minute preheating phase, ensuring drying equipment reaches the predetermined parameters, the sliced Rhubarb was placed into the ultrasound synergistic hot-air drying equipment.During the drying process, the sample quality is to be measured every 30 min and then promptly returned to the drying chamber to continue drying until the moisture content of the sample reaches the safe storage moisture content of 12.00% [21].SD group served as the blank control group, with samples placed in an environment characterized by exposure to sunlight and dry ventilation.All experimental samples underwent ultrasound synergistic hot-air drying except for SD.In instances where variable-frequency ultrasound treatment was employed, the ultrasonic frequency underwent precise adjustments at specified time nodes.Each experimental condition was repeated three times, and the results were averaged from three sets of data.
The preliminary experiments determined that the optimal conditions for ultrasound synergistic hot-air drying of Rhubarb slices included a temperature of 55 • C), ultrasonic power of 120 W, and the utilization of both constant-frequency and variable-frequency ultrasound modes.In the constant-frequency mode serving as the conditional control group, frequencies of 25 kHz, 28 kHz, and 40 kHz were tested.The study primarily focuses on investigating the effect of segmented variablefrequency ultrasound on the drying characteristics and quality.The selection of time nodes for frequency conversion is comprehensively based on the consideration of both the shrinkage rate and drying rate during the drying process of Rhubarb slices.Fig. 2 illustrates the physical shape changes of Rhubarb at different time points during constant-frequency ultrasound treatment, with the corresponding drying rate curve of Rhubarb under the same conditions shown in Fig. 3 (b).Based on the comparison of shrinkage rates during the drying process in the control group (Fig. 2), it is evident that the average shrinkage rate of the samples is lowest when subjected to the 25 kHz condition within the initial 0 to 60-minute timeframe of the drying process.Subsequently, during the 60 to 120-minute timeframe, the sample average shrinkage rate is the lowest under 28 kHz conditions.Beyond the 120-minute mark, the sample average shrinkage rate is the minimum under 40 kHz conditions.The contraction reaction induced by drying can affect the moisture stress, leading to cracking and collapse of materials, consequently diminishing the quality of dried products [22,23].Therefore, in light of minimizing the impact of shrinkage, a frequency combination with less shrinkage effect is considered, with 60 min and 120 min selected as a pair of time nodes for frequency conversion.From a drying rate perspective, Fig. 3(b) illustrates that during the initial 1/2 stage of the    drying process (90 min prior), the drying rate of samples under the 40 kHz condition is notably faster compared to those under 25 kHz and 28 kHz conditions.This highlights a distinct advantage of ultrasonic treatment at 40 kHz.However, after 150 min of drying, the drying rate of samples under 40 kHz ultrasonic action starts to be lower than that under 25 kHz.It can be seen that different ultrasonic frequencies are suitable for Rhubarb at different time periods, with 90 min and 150 min being critical nodes where the drying rate undergoes a significant transition.In summary, the time points of 60 min and 120 min were selected as the time nodes for frequency conversion when considering the shrinkage rate, while 90 min and 150 min were selected as the time nodes for frequency conversion when considering the drying rate.These time nodes were utilized to investigate the effects of SVFU-HAD on the drying characteristics and quality of Rhubarb.The sequence of frequency conversion comprises two modes: the upscaled-frequency ultrasound (UFC) from low-frequency to high-frequency and the reduced-frequency ultrasound (RFC) from high-frequency to low-frequency.The specific variable-frequency processing schemes are outlined in Table 1.

Calculation of drying parameters 2.4.1. Dry basis moisture content
The dry basis moisture content in the drying process of Rhubarb was calculated according to Eq. ( 1) [24]: Where M t is the dry basis moisture content of Rhubarb at time t, g/g; m t is the quality of Rhubarb at time t, g; m g is the quality of Rhubarb dry matter, g.

Drying rate
The drying rate, representing the change in moisture content of the Rhubarb sample over each time interval during the drying process, can be calculated as follows Eq. ( 2) [25]: Where V R is the drying rate of the Rhubarb, g/(g•min); t 1 and t 2 are any drying time, min; M t1 is the dry basis moisture content of Rhubarb at time t 1 , g/g; M t2 is the dry basis moisture content of Rhubarb at time t 2 , g/g.

Ultrasonic cavitation field
The ultrasonic cavitation field distribution was assessed using the dyeing method [26] under various conditions.A 5 mg/mL aqueous solution of methylene blue was prepared and added to the material tray while the coated paper was positioned horizontally.Subsequently, constant-frequency ultrasound at 25 kHz, 28 kHz, and 40 kHz, as well as variable-frequency ultrasound, were applied successively.Each frequency of ultrasound was allowed to act for 1 min before the coated paper was removed for observation.

Rehydration ratio
The dried Rhubarb samples were subjected to a controlled temperature water bath at 40 • C) for a duration of 130 min, following which they were removed.The surface moisture of the Rhubarb slices was repeatedly absorbed using absorbent paper until the weight remained constant.The weight of the Rhubarb was then measured.The formula for calculating the rehydration ratio is as follows Eq. ( 3) [27]: Where RR is the rehydration ratio; M f is the weight of dried Rhubarb products after rehydration, g; M 0 is the weight of dried Rhubarb products before rehydration, g.

Microstructure
Under the premise of protecting the observation surface, dried samples of Rhubarb approximately 6 mm × 4 mm × 3 mm in size were taken and pasted onto a metal sample stage using conductive adhesive.Two 60-second coating treatments were then performed using ion sputtering.The resulting microstructures of Rhubarb were observed under various conditions using an S3400N scanning electron microscope at a magnification of 300 times.

Color difference
The CR-410 colorimeter was adopted to detect the color of dried samples under different drying methods.The total color difference ΔE was employed to indicate the variation in color between the tested samples and the fresh sample, which was calculated following Eq.( 4) [28]: Where L*, a*, and b* represent the lightness value, red-green value, and yellow-blue value of dried Rhubarb samples, respectively.L* 0 , a* 0 , and b* 0 represent the brightness value, red-green value, and yellow-blue value of the Rhubarb fresh sample, respectively.ΔE represents the total color difference between the dried samples and the fresh sample.

Bioactive compounds 2.9.1. Preparation of sample extracts
The dried Rhubarb samples were pulverized and sieved through a 60mesh screen.Approximately 0.5 g ± 0.05 g of the resulting powder was weighed and placed into a 50 mL conical centrifuge tube, followed by the addition of 25 mL of 75% ethanol (V/V).The tube was then positioned in a light-protected shaker and continuously oscillated for 48 h.Following this period, the mixture was centrifuged for 10 min at a speed of 3000 rpm and a temperature of 26 • C.

Determination of total phenolic content
Following the methodology outlined by Beato et al. [29], adhering to the Folin-Ciocalteu reagent method, the total phenolic content of the Rhubarb samples was assessed.Specifically, 10 μL of the extract was aspirated, followed by the sequential addition of 2.0 mL of 10% Folin-Ciocalteu reagent and 1.0 mL of 7.5% Na 2 CO 3 .During the reaction process, the test tube solution changed from the initial extract color to yellow upon the addition of Folin-Ciocalteu.Subsequently, after the addition of Na 2 CO 3 , the reaction mixture was placed in a water bath at 37 • C) in the dark for 1 h to allow for a complete reaction, during which the reaction solution gradually turned blue-gray.In order to establish the standard curve of total phenols, gallic acid was employed as the reference standard:

Table 1
Experimental schemes for SVFU-HAD.The formula for calculating the total phenolic content is as follows Eq. ( 5):

Time nodes of frequency conversion
Where A is the absorbance value of the sample solution; C 1 is the concentration of total phenols, mg/mL; TPC is the total phenolic content, mg/g⋅DW; M is the dry matter weight of the weighed Rhubarb, g; V is the volume of the extract, mL; D 1 is the dilution multiple of the extract for the determination of total phenolic compounds content.

Determination of total flavonoids content
Drawing on the measurement method proposed by Ma et al. [30], the total flavonoids content of the samples was determined through the use of the sodium nitrite-aluminum chloride-sodium hydroxide method.
Initially, a volume of 100 μL of the extraction solution was taken to determine the total flavonoids content of the Rhubarb samples.Sequentially, 2.0 mL of distilled water, 0.3 mL 5.0% NaNO 2 , 0.3 mL 10% AlCl 3 , and 2.0 mL 1 mol/L NaOH were added.During the reaction process, the test tube solution was initially colorless, turned yellow upon the addition of AlCl 3 , and gradually transformed into red upon the addition of NaOH.In order to establish the standard curve for total flavonoids, Catechin was utilized as the reference standard: The formula for calculating the total flavonoids content is as follows Eq. ( 6): Where C 2 is the concentration of total flavonoids, mg/mL; TFC is the total flavonoids content, mg/g⋅DW; D 2 is the dilution multiple of the extract for the determination of total flavonoids compounds content.

Determination of total sugar content
The total sugar content of the sample was determined using the phenol-sulfuric acid method, referencing the measurement technique outlined by Dubois et al. [31].The sample extraction solution of 5 μL was placed in a test tube, followed by the sequential addition of 1.0 mL 9.0% phenol solution and 3.0 mL concentrated sulfuric acid.After thorough mixing and reaction, the test tube solution changed from colorless to reddish-orange.To establish a reliable standard curve for quantifying the total sugar content, sucrose was utilized as the reference standard: The formula for calculating the total sugar content is as follows Eq. ( 7): Where C 3 is the concentration of total sugar, mg/mL; TSC is the total sugar content, mg/g⋅DW; D 3 is the dilution multiple of the extract for the determination of total sugar content.

Determination of antioxidant capacity
The antioxidative capacity of the sample was determined using the DPPH method, employing the protocol outlined by Nencini et al. [32].
The inhibitory rate of Rhubarb samples was determined by adding 5 μL of the extraction, followed by the addition of 3.0 mL of 10 − 4 mol/L DPPH.The reaction should then be allowed to oscillate in darkness at room temperature for 30 min.During the reaction, the solution in the test tube gradually changed from purple to a lighter shade.A lighter color suggests a higher inhibition rate, signifying a stronger antioxidative capacity in the sample.
The Inhibitory rate was calculated by Eq. ( 8): Where I represents the inhibitory rate of the sample solution; A 0 represents the absorbance value of the solution without the sample.

Natural active ingredients
Preparation of HPLC sample extract [33]: accurately weigh 0.5 ± 0.005 g of Rhubarb powder passed through a 60-mesh sieve.Place it in a conical centrifuge tube and add precisely 25 mL of 60% methanol (V/V).Perform ultrasonic extraction for 1 h (at a frequency of 40 kHz and power of 210 W), followed by centrifugation for 10 min (at a temperature of 26 • C and a speed of 3000 rpm).Filter the extract (using a 0.45 μm microporous membrane) and transfer 0.5-1.5 mL into a 2 mL vial for the sample bottle.
Preparation of single reference standards: the preparation of nine single reference standards was conducted to determine the retention times of nine natural active ingredients.Single reference standard stock solutions were prepared for gallic acid, cyanidanol, sennoside A, sennoside B, aloe emodin, rhein, emodin, chrysophanol, and emodin-3methyl ether, each attaining a purity of ≥98% and a concentration of 1 mg/mL.3 mg of each compound were dissolved in 3 mL of HPLC methanol.Subsequently, 0.3 mL of each single reference standard stock solution was combined with 0.7 mL of HPLC-grade methanol to yield nine single reference standard solutions, each boasting a concentration of 0.3 mg/mL.
Preparation of mixed reference standards: nine concentrations of mixed reference standards were prepared to establish a standard curve by plotting the relationship between the different concentrations and the corresponding peak areas measured by HPLC.Firstly, 1 mL aliquots of each of the nine single reference standard stock solutions were amalgamated in a test tube and shaken to generate a composite reference standard solution 1, with a concentration of 0.111 mg/mL for each constituent ingredient.Subsequently, composite reference standard solution 2 was formulated by combining 1 mL of composite reference standard solution 1 with 1 mL of HPLC-grade methanol, yielding a concentration of 0.056 mg/mL for each functional ingredient.This process was iterated to generate composite reference standard solutions 3, 4, 5, and 6, ensuring a comprehensive range of concentrations for subsequent analysis.

Thermal simulation of drying process
As the drying process progresses, internal temperature variations occur within the Rhubarb slices.This study aimed to examine the influence of ultrasound on heat transfer in materials and to visually depict the uniformity of hot-air drying and ultrasound synergistic hot-air drying.A heat transfer model was developed using the mechanical module of ANSYS Workbench software to achieve this.The model was designed to simulate the temperature dynamics of Rhubarb slices under different drying conditions and time intervals, thereby illustrating the temperature changes during the drying process.
The modeling process was based on the following assumptions: (1) The wall of the electrothermal blowing dry box serves as an insulator with no heat dissipation.(2) Rhubarb is treated as an isotropic material.
(3) Apart from the heat required for water evaporation from Rhubarb slices, all other heat is used for material heating.(4) Neglecting the X.Ying et al.
impact of power loss heat from the ultrasonic transducer on the slicing of Rhubarb.The thermal supply and dissipation within individual material systems adhere to the law of energy conservation, which can be described by Eq. ( 9): The specific modeling process is outlined as follows.
Firstly, the 3D model of Rhubarb was established, material properties were defined, automatic mesh generation was performed, and the initial material temperature was set.
Next, boundary conditions for hot air convection were established.Newton's law of cooling was applied to describe the convective heat transfer in hot-air drying.According to this law, in forced convection scenarios, the rate of heating or cooling of an object is primarily influenced by the ambient temperature rather than its specific physical and chemical properties.The fundamental formula is represented by Eq. ( 10) [34]: The drying process involves mass transfer, where the heat dissipation required for moisture evaporation within Rhubarb slices, denoted as Q 2 , must be considered in simulations to emulate actual conditions.Each drying process is subject to the superimposition of the Heat Flux environment.The formula for calculating Q 2 is provided as Eq. ( 11) [35]: Where w is the accumulated water evaporation during the drying period, 2492 kJ/kg is the approximate value of water vaporization heat.4.187T 0 w is the heat brought into the system by moisture in the material, the value of which is relatively small and can be neglected.Eq. ( 10) is simplified to Eq. ( 12): Furthermore, a model of ultrasound-assisted drying can be established on the basis of the hot-air drying environment.According to the thermal mechanism of ultrasound, the waves absorbed by the material during the ultrasonic propagation process convert the acoustic energy of ultrasound into internal heat energy Q 3 through mechanical action.The calculation formula is as shown in Eqs. ( 13)-( 15) [8]: The calculation formula for acoustic energy density I is Eq. ( 14): The calculation formula for acoustic pressure amplitude P A is Eq. ( 15): It is worth noting that the variable-frequency ultrasound in this section needs to consider different ultrasonic frequencies at different stages.The meanings and units of the variables involved in Eqs. ( 9)-( 15) are shown in Table 2.

Statistical processing and analysis
The experimental data refinement was carried out using Microsoft Excel (Redmond, WA, USA), OriginLab (Northampton, MA, USA), and SPSS (Chicago, IL, USA).The data results were analyzed using one-way analysis of variance (ANOVA), subjected to the Duncan test and homogeneity of variance test, with the mean ± standard deviation represented.When P < 0.05, differences in the mean values of the data were considered statistically significant.

Effect of SVFU-HAD on the drying characteristics of Rhubarb slices
The drying characteristic curves of Rhubarb slices under the conditions of three constant-frequency ultrasound synergistic hot-air drying (CFU-HAD) and four SVFU-HAD are shown in Fig. 3.As illustrated, within constant-frequency ultrasound drying, the highest drying rate occurs at 40 kHz, whereas the lowest is observed at 25 kHz.Furthermore, four types of segmented variable-frequency ultrasound drying exhibit reduced drying times compared to 25 kHz constant-frequency ultrasound drying.At 180 min, the dry basis moisture content of samples treated with two types of UFC was lower than that of samples treated with 25 kHz and 28 kHz constant-frequency ultrasonic treatment (Fig. 3(a)), indicating that samples treated with UFC reached the safe dry basis moisture content faster than those treated with 25 kHz and 28 kHz constant-frequency ultrasonic treatment.This could be attributed to the fact that variable-frequency ultrasound is more effective than constant-frequency ultrasound in promoting the formation of micropores and increasing the rate of dehydration [20].The drying time of samples subjected to the action of two different RFC and 40 kHz constant-frequency ultrasound was found to be essentially equivalent, with no significant difference in the average drying rate among the three treatments (P > 0.05).The slope of the drying rate during the deceleration period serves as a gauge for the rate of decline in the drying rate, with a larger slope indicating a swifter decrease and a smaller slope suggesting a more gradual decline.Under the UFC1 drying conditions, the drying rate slope between 30 min and 60 min is 1.878 times that between 60 min and 90 min.Under RFC2 drying conditions, the drying rate slope between 60 min and 90 min is 1.485 times that between 90 min and 120 min.This indicates that variable-frequency ultrasound, to some extent, attenuates the decreasing trend of the drying rate.Xu et al. [18] have also found that variable-frequency ultrasound can more effectively promote mass transfer, primarily due to the replacement of the pulse intervals of constant-frequency ultrasound by another ultrasound frequency.
This study utilized the dyeing method to characterize the cavitation field in order to investigate the distinct effects of constant-frequency and variable-frequency ultrasonic cavitation.As depicted in Fig. 4, an increase in ultrasonic frequency results in finer and denser cavitation effect points.Moreover, compared to constant-frequency ultrasound, variable-frequency ultrasound yields a more uniform cavitation field with a higher density of cavitation effect points.This finding aligns with previous studies utilizing the aluminum foil corrosion method and hydrophone measurements [18,36].Under variable-frequency ultrasound conditions, bubbles of different frequencies within the slices of Rhubarb occur, creating a vibrational phenomenon, activating more bubble activity and forming a larger effective cavitation area.Therefore, the cavitation effect generated by variable-frequency ultrasound is superior to constant-frequency ultrasound, optimizing the ultrasonic excitation effect, thus further affecting product quality.

Effect of different drying conditions on rehydration ratio
Many scholars believe that the rehydration ratio of dried products is primarily related to the varying degrees of damage or changes in microstructure due to different stresses within the internal cells and structures during the drying process [37].Table 3 provides insights into the rehydration ratio of Rhubarb samples under different drying conditions, while Fig. 5 illustrates the microstructure of Rhubarb samples under different drying conditions.Observing Table 3 reveals that the rehydration ratio of Rhubarb slices increases with the rise of ultrasonic frequency.This phenomenon is likely attributed to the enhanced mechanical action on the Rhubarb slices with increasing ultrasonic frequency, leading to continuous expansion and contraction of cell tissues, thereby promoting the formation of micro-pores [38].Consequently, the cell tissues of Rhubarb slices become loose (as shown in Fig. 5(a)-(c)),  which facilitates the absorption of more water, thus improving the rehydration ratio.Also, from Table 3, it is evident that the samples subjected to RFC2 variable-frequency processing exhibit the best rehydration ratio.From a microscopic perspective, as analyzed in Fig. 5(f), under this ultrasonic processing condition, the damage to the sample's microporous structure is relatively minor.Research by Azam et al. [39] also indicates that samples subjected to triple-frequency sequential processing experience less mechanical damage.In comparison, samples processed with RFC1 and SD exhibited poorer rehydration ratios.Fig. 5 (d) and (e) depict distinct cracks in the SD samples, while noticeable shrinkage deformation is observed in samples processed with RFC1, likely contributing to their poor rehydration ratios.Furthermore, in samples subjected to variable-frequency ultrasonic treatment, the two groups of samples with 90 min and 150 min as the time nodes for frequency conversion demonstrated enhanced rehydration properties.This may be due to the fact that the variable-frequency ultrasonic combination according to the drying rate dividing frequency helped to improve the effect of ultrasound on the structure of Rhubarb slices, which resulted in the improvement of the rehydration ratio of the dried Rhubarb products.

Effect of different drying conditions on color appearance
The parameter ΔE serves as an objective indicator of the appearance quality of dried products.A lower ΔE value corresponds to a higher appearance quality of dried products, thereby increasing consumer purchasing desire.Furthermore, the traits of medicinal herbs serve as an objective reflection of intrinsic quality.Consequently, the ΔE value, to a certain degree, elucidates the relative abundance of natural bioactive constituents nestled within Rhubarb.
As illustrated in Fig. 6, the distance value between the points of dried Rhubarb products under different conditions and fresh sample point in the space Cartesian coordinate system corresponds to the ΔE value of the dried products.Notably, the ΔE value demonstrates a general uptrend with the escalation of ultrasonic frequency under constant-frequency ultrasound, as can be seen in Fig. 6.This phenomenon can be attributed to the higher ultrasonic frequency, which amplifies the mechanical effects within the Rhubarb, resulting in the formation of additional micro-pores [38].This facilitates the migration of substances within the Rhubarb, resulting in the loss of internal pigment components in Rhubarb, consequently causing an increase in the ΔE value.Furthermore, the Rhubarb dried product exhibits negative values for overall Δa* and Δb*, which may be attributed to the fact that anthocyanins and cell sap were released into the intercellular space during the drying process, where anthocyanins turn bluish-green when they encounter the alkaline Rhubarb cell sap [40].The ΔE value of dried samples treated by RFC is smaller than that of the dried samples treated by UFC, while the ΔE value of SD samples is the largest, which is related to the drying duration.Kowalski et al. [41] also observed that a shorter drying time has a protective effect on the color of dried products.Additionally, it can be observed that the ΔE values of dried samples treated with variable frequency at the critical time nodes of drying rate transition (90 min and 150 min) are smaller compared to those treated with variable frequency at the critical time nodes of shrinkage rate transition (60 min and 120 min).It is noteworthy that the dried samples treated with RFC1 show the smallest values for Δa* (− 3.56) and Δb* (3.74), while those treated with RFC2 exhibit the smallest value for ΔL* (− 2.03).This indicates that the variable-frequency method of RFC can better preserve the color of Rhubarb.

Effect of different drying conditions on TPC, TFC, TSC, and antioxidant capacity
The total phenolic content, total flavonoids content, total sugar content, and antioxidant capacity play a significant role in the efficacy of Rhubarb.Fig. 7 delineates these parameters across varied ultrasonic frequency conditions.Remarkably, under RFC1 conditions, the total flavonoids content and antioxidant capacity of Rhubarb samples are only slightly lower than those of SD samples, with total phenolic content reaching as high as 82.215 mg/g, exceeding that of SD samples.It is evident that the RFC1 variable-frequency condition has a positive effect on ameliorating the total phenolic content, total flavonoids content, and antioxidant capacity of Rhubarb through ultrasound synergistic hot-air drying.This phenomenon can be attributed to the higher ultrasonic frequency in the initial stage, which increases microporosity, thereby facilitating the subsequent release of total phenols and total flavonoids.Subsequently, in the second and third stages, the prolonged application of low-frequency ultrasound enables deeper tissue penetration, progressively releasing additional phenolic compounds.In contrast, samples treated with RFC2 and 28 kHz constant-frequency ultrasound exhibited lower total phenolic and total sugar content (60.406 mg/g, 65.928 mg/g, and 260.327 mg/g, 305.322 mg/g, respectively), samples treated with UFC1 and RFC2 showed lower total flavonoids content (37.139 mg/g, 37.014 mg/g), and samples treated with RFC2 and 25 kHz constant-frequency ultrasound displayed lower antioxidant capacity (41.25%, 43.72%).These findings indicate a significant negative impact of RFC2, UFC1, 28 kHz constant-frequency, and 25 kHz constantfrequency ultrasound treatments on the retention of total phenols, total flavonoids, total sugars, and DPPH free radicals in Rhubarb.Under the conditions of RFC2, the total phenolic and total sugar content in dried products are relatively low.This could be due to insufficient lowfrequency action time in the later stage, resulting in a decrease in the release rate of total phenolic and total sugar.Nevertheless, Tao et al. [42] found that excessively long low-frequency ultrasonic action time may lead to ingredient degradation.Therefore, it is crucial to balance the action time of different frequencies during the process of frequency conversion.In addition, it was observed that the overall trends in changes of total flavonoids and total phenolic content were generally consistent with the antioxidant capacity, indicating a correlation between total phenolic and total flavonoids content with antioxidant capacity, in line with the research results of Claudia and Zhang et al. [43,44].

Effect of different drying conditions on the natural active ingredients
The natural active ingredients such as free anthraquinones, tannins, and dianthrones in Rhubarb exhibit significant biological activities.Among these, free anthraquinones demonstrate antibacterial and antiinflammatory effects, tannins possess anticoagulant properties, and dianthrones are the primary components responsible for the laxative effects of Rhubarb [45][46][47][48].These three types of components show significant biological activity within Rhubarb.Under different ultrasonic frequency conditions, the content of tannins, dianthrones, and free anthraquinones is illustrated in Fig. 8. Upon observation, it is noted that under the conditions of UFC1 treatment, the content of tannins, dianthrones, and free anthraquinones are the lowest, rendering it unsuitable for the drying of Rhubarb.Under variable-frequency processing conditions, the average content of tannins, dianthrones, and free anthraquinones are 3.51%, 4.32%, and 10.97% higher, respectively, compared to constant-frequency conditions.This phenomenon is attributed to the heightened cavitation nuclei generation facilitated by variable-frequency ultrasound (seen in Fig. 4), thereby enhancing the dissociation of gallic acid, cyanidanol, and free anthraquinones from their respective complexes.When comparing SVFU-HAD and CFU-HAD with SD experiments, it was observed that the samples with the least loss in tannins, dianthrones, and free anthraquinones were consistently the samples treated with RFC.Especially noteworthy is the minimal loss of dianthrones and free anthraquinones components, processed through RFC1, amounting to 6.95% and 6.45%, respectively.Under this variablefrequency condition, the content of tannins, dianthrones, and free anthraquinones exceed the average values of the other experimental groups by 3.24%, 26.65%, and 14.42%, respectively.It can be observed that the RFC1 treatment mode plays a positive role in retaining the natural active ingredients of Rhubarb.This phenomenon may be attributed to the enhanced mutual conversion of the compounds with these natural active ingredients in the RFC1 variable-frequency environment, thereby leading to a higher in their content [49].Collectively, it can be observed that different drying processes significantly alter the natural active ingredients content of Rhubarb slices, with samples treated with RFC1 showing the best overall effect.

Thermal simulation results analysis
The simulated temperature distribution cloud diagram of the Rhubarb drying process under different conditions is shown in Fig. 9. Comparing the simulation results of RFC1 in Fig. 9(a) and (b) with the thermal images of RFC1 obtained through thermal imager (as shown in Fig. 10), it is evident that at 60 min and 120 min, the observed temperatures are 37.9 • C and 48.5 • C, respectively, consistent with the simulated temperature range of Rhubarb slices (36.066 • C-41.798 • C and 48.395 • C-50.462 • C. Further analysis of the thermal imaging temperature and simulation temperature at different times of RFC1, as shown in Fig. 11, reveals that the relative error between the average values of simulated and observed temperatures at each time point is within 5%, with a good degree of agreement and the changing trend being basically consistent, indicating the simulation results are reliable under certain conditions.Therefore, it can be seen that the simulation model can be used to simulate and predict the heat transfer phenomenon of ultrasound synergistic hot-air drying under certain conditions, aiding in resolving heat-related issues during the drying process and improving the quality of dried products.
The heat source for ultrasound synergistic hot-air drying of Rhubarb involves two main aspects: the convective heat transfer generated by hot air and the ultrasonic thermal effect.The latter entails the propagation of ultrasonic waves within the material, inducing friction within its structure, thus converting acoustic energy into heat energy and consequently elevating the temperature of Rhubarb.In contrast to conventional hot-air drying methods, the SVFU-HAD demonstrates an average temperature escalation of 4.436 • C and 5.608 • C at 60 min and 120 min, respectively, as illustrated in Fig. 9.This observed phenomenon can be ascribed to the efficient absorption of ultrasonic energy by Rhubarb slices, which accelerates the drying process compared to conventional methodologies.From the maximum and minimum temperature variations in the heat transfer simulation model of the RFC1 synergistic hotair drying Rhubarb shown in Fig. 11, it can be seen that the temperature difference of the drying process gradually increases and then decreases.Furthermore, as observed in Fig. 9, compared to hot-air drying and CFU-HAD, when Rhubarb slices are subjected to SVFU-HAD, the overall temperature can reach a relatively stable state more quickly, thereby improving the uniformity of drying heat transfer.This is because, for one thing, the heat of hot-air drying is transferred from the surface of the material to the interior, while the heat in ultrasound-assisted drying acts on the interior of the material.The synergistic effect of these two methods helps in redistributing the temperature, thus improving the uniformity of drying [50,51].Additionally, compared to constant frequency ultrasound, variable frequency ultrasound requires less time to reach the voltage amplitude, which can more quickly generate cavitation effects, reduce the moisture diffusion resistance in the material, accelerate the drying efficiency, and improve the uniformity of drying [18].

Conclusion
This study combined segmented variable-frequency ultrasound with hot-air drying to compare the drying characteristics and quality of Rhubarb slices under different constant-frequency and variablefrequency ultrasound treatment conditions.The results indicate that compared to CFU-HAD, SVFU-HAD contributes to optimizing the cavitation effect and enhancing the drying characteristics.In terms of rehydration ratio, the Rhubarb dried products treated with 90 min and 150 min as time nodes of frequency conversion demonstrate advantages, with values of 3.328 ± 0.061 and 3.377 ± 0.051, respectively.The utilization of RFC variable-frequency ultrasound treatment can decrease ΔE value by at least 14.83%, which contributes to maintaining the color of Rhubarb.Among the seven ultrasound synergistic hot-air drying methods, RFC1 demonstrates a more pronounced overall performance in preserving the content of bioactive components, such as TPC and free anthraquinones.Furthermore, this study utilized ANSYS Workbench software to simulate the heat transfer process, demonstrating a good agreement between simulated and observed values with a relative error in average temperature of less than 5%.The simulation results indicate that compared to HAD and CFU-HAD, SVFU-HAD exhibits better drying uniformity.Overall, the RFC1 drying method is more effective in enhancing the drying efficiency and improving the quality of dried products.Combining the aforementioned results indicates that the rational application of segmented variable-frequency ultrasound technology can more effectively harness the ultrasonic effects.This study serves as a compelling testament to the substantial promise of segmented variable-frequency ultrasound in elevating the efficacy of ultrasound synergistic hot-air drying, thereby offering invaluable insights for augmenting the industrial value of ultrasound-assisted drying techniques and optimizing the caliber of dried products.

Fig. 2 .
Fig. 2. Physical shape changes of the Rhubarb drying process under the constant-frequency ultrasound of 25 kHz, 28 kHz, and 40 kHz.(Shrinkage (%) = ((A 0 − A 1 )/ A 0 ) × 100, A 0 is the area of the Rhubarb slice in the first 30 min, A 1 is the area of the Rhubarb slice at the current moment).Symbolize markers of frequency conversion.

Fig. 3 .
Fig. 3. Dry basis moisture content curve (a) and drying rate curve (b) of Rhubarb under different ultrasonic frequency conditions.

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. Ying et al.

Fig. 4 .
Fig. 4. Dye adhesion situation on coated paper under different ultrasonic frequency conditions.

Fig. 7 .
Fig. 7. Total phenolic, total flavonoid, total sugar content, and antioxidant capacity of Rhubarb under different ultrasonic frequency conditions.

Fig. 9 .
Fig. 9. Simulation temperature distribution contours of Rhubarb slices under different drying conditions.

Fig. 11 .
Fig. 11.Thermal imaging temperatures and simulated temperatures at different moments of Rhubarb under RFC1 condition.

Table 2
List of symbols.

Table 3
Rehydration ratios of Rhubarb samples under different drying conditions.
X. Ying et al.